The invention is based on a device for measuring the mass of a flowing medium as set fourth hereinafter. A device is already known (German Published Patent Disclosure DE-OS 36 38 138, now U.S. Pat. No. 4,777,820), in which a so-called hot-film sensor element is placed in a flowing medium and, to measure the flow rate of the flowing medium, has a temperature-dependent sensor region composed of individual resistor layers applied to a platelike substrate and including at least one heating resistor and at least one temperature-dependent measuring resistor. For measurement, the measuring resistor is kept at an overtemperature that is far above the temperature of the flowing medium, so that substantially because of convection, it gives off a certain amount of heat to the flowing medium as a function of the mass or flow rate of the flowing medium moving past it. The heating resistor, in a known manner, serves to maintain the constant overtemperature of the measuring resistor and is disposed in the best possible thermal contact with the measuring resistor so as to raise the temperature of the latter resistor as fast as possible. The measuring resistor has a resistance that is dependent on the temperature, so that a change in the overtemperature causes a change in its resistance, and a closed-loop control circuit connected to the measuring resistor and the heating resistor is mistuned. The closed-loop control circuit is embodied for instance as a bridgelike resistance measuring circuit that upon being mistuned by the measuring resistor varies the heating current or heating voltage of the heating resistor, so as to keep the overtemperature of the measuring resistor constant; the heating current or heating voltage of the heating resistor required for maintaining the overtemperature of the measuring resistor is a standard for the mass of the flowing medium. As may be learned from the prior art referred to at the outset, the substrate has a further resistor, which will hereinafter be called the medium temperature resistor and which is disposed on the substrate; it is thermally decoupled from the heating resistor and the measuring resistor by means of slits made by removal of material from the substrate. The medium temperature resistor has a resistance that is dependent on the temperature and is part of the closed-loop control circuit that assures that changes in the temperature of the flowing medium do not affect the measurement accuracy of the device. Because of the nearness of the medium temperature resistor to the heating resistor, thermal influence cannot be entirely precluded, however, since despite the slits recessed from the substrate, heat flows can result within the substrate that can flow, for instance via a retainer of the hot-film sensor element, to the medium temperature resistor, causing it not to assume precisely the temperature of the flowing medium. Moreover, the heat flows not delivered to the flowing medium by the heating resistor have the effect that the response time of the device to changes in the temperature of the flowing medium is slowed down. In the case of a pulsating flow with a partial reverse flow at the hot-film sensor element, it can also happen that heated medium from the heating resistor reaches the medium temperature resistor, causing the latter to incorrectly assume a temperature of the flowing medium that has been increased by the heating resistor.